{"id":"https://openalex.org/W2026775156","doi":"https://doi.org/10.1142/s1793830914500219","title":"THE DOMINATION NUMBER OF STRONG PRODUCT OF DIRECTED CYCLES","display_name":"THE DOMINATION NUMBER OF STRONG PRODUCT OF DIRECTED CYCLES","publication_year":2014,"publication_date":"2014-01-23","ids":{"openalex":"https://openalex.org/W2026775156","doi":"https://doi.org/10.1142/s1793830914500219","mag":"2026775156"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830914500219","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830914500219","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076343828","display_name":"Huiping Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I1334729051","display_name":"Xinjiang Normal University","ror":"https://ror.org/00ndrvk93","country_code":"CN","type":"education","lineage":["https://openalex.org/I1334729051"]},{"id":"https://openalex.org/I102208913","display_name":"Shihezi University","ror":"https://ror.org/04x0kvm78","country_code":"CN","type":"education","lineage":["https://openalex.org/I102208913"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"HUIPING CAI","raw_affiliation_strings":["Department of Mathematics, College of Sciences, Shihezi University, Shihezi, Xinjiang, 832003, P. R. China","School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang, 830054, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Sciences, Shihezi University, Shihezi, Xinjiang, 832003, P. R. China","institution_ids":["https://openalex.org/I102208913"]},{"raw_affiliation_string":"School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang, 830054, P. R. China","institution_ids":["https://openalex.org/I1334729051"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100446326","display_name":"Juan Liu","orcid":"https://orcid.org/0000-0003-0857-3877"},"institutions":[{"id":"https://openalex.org/I1334729051","display_name":"Xinjiang Normal University","ror":"https://ror.org/00ndrvk93","country_code":"CN","type":"education","lineage":["https://openalex.org/I1334729051"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JUAN LIU","raw_affiliation_strings":["School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang, 830054, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang, 830054, P. R. China","institution_ids":["https://openalex.org/I1334729051"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083875448","display_name":"Lingzhi Qian","orcid":null},"institutions":[{"id":"https://openalex.org/I102208913","display_name":"Shihezi University","ror":"https://ror.org/04x0kvm78","country_code":"CN","type":"education","lineage":["https://openalex.org/I102208913"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"LINGZHI QIAN","raw_affiliation_strings":["Department of Mathematics, College of Sciences, Shihezi University, Shihezi, Xinjiang, 832003, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Sciences, Shihezi University, Shihezi, Xinjiang, 832003, P. R. China","institution_ids":["https://openalex.org/I102208913"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5076343828"],"corresponding_institution_ids":["https://openalex.org/I1334729051","https://openalex.org/I102208913"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.08956797,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"06","issue":"02","first_page":"1450021","last_page":"1450021"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9753000140190125,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9735000133514404,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.8550822734832764},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8169959783554077},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6547869443893433},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.6518796682357788},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6387096047401428},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.6358078718185425},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.6049054861068726},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.16241061687469482},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.14221417903900146},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.07464629411697388},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06889334321022034},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06631916761398315}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.8550822734832764},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8169959783554077},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6547869443893433},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6518796682357788},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6387096047401428},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.6358078718185425},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.6049054861068726},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.16241061687469482},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.14221417903900146},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.07464629411697388},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06889334321022034},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06631916761398315},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830914500219","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830914500219","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W71943752","https://openalex.org/W1963704255","https://openalex.org/W1993642211","https://openalex.org/W1994365837","https://openalex.org/W2023782877","https://openalex.org/W2036674522","https://openalex.org/W2057389336","https://openalex.org/W2074999109","https://openalex.org/W2104479384"],"related_works":["https://openalex.org/W2038088825","https://openalex.org/W2921632378","https://openalex.org/W1975203667","https://openalex.org/W2964086477","https://openalex.org/W2034343496","https://openalex.org/W4300480352","https://openalex.org/W2086198191","https://openalex.org/W2038795318","https://openalex.org/W229639882","https://openalex.org/W4210490117"],"abstract_inverted_index":{"Let":[0],"\u03b3(D)":[1],"denote":[2,17],"the":[3,18,28,42,99],"domination":[4],"number":[5],"of":[6,21,31,58,84,98],"a":[7,51],"digraph":[8],"D":[9],"and":[10,24,54,73],"let":[11],"C":[12,15,22,25,63,69],"m":[13,23,60,64,70,88,92,104,107,111],"\u2297":[14,62,66,68],"n":[16,26,34,71,93,112],"strong":[19],"product":[20],",":[27,87,90,106,109],"directed":[29],"cycles":[30],"length":[32],"m,":[33],"\u2265":[35],"2.":[36],"In":[37],"this":[38],"paper,":[39],"we":[40,49,101],"determine":[41],"exact":[43],"values":[44],"[Formula:":[45,76],"see":[46,77],"text]":[47,78],"Furthermore,":[48],"give":[50],"lower":[52],"bound":[53,57],"an":[55],"upper":[56],"\u03b3(C":[59],"1":[61,86],"2":[65,89],"\u22ef":[67],")":[72],"obtain":[74],"that":[75,103],"when":[79],"at":[80],"least":[81],"n-2":[82],"integers":[83],"{m":[85],"\u2026,":[91,110],"}":[94],"are":[95,113],"even":[96],"(because":[97],"isomorphism,":[100],"assume":[102],"3":[105],"4":[108],"even).":[114]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}